A350836 - OEIS

A350836

Numbers k such that A103168(k) = A340592(k).

1, 2, 3, 5, 7, 11, 14, 50, 101, 131, 151, 181, 191, 194, 313, 353, 373, 383, 712, 727, 757, 762, 787, 797, 919, 929, 1100, 1994, 2701, 4959, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661, 17471, 17971, 18181

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OFFSET

1,2

COMMENTS

Numbers k such that the concatenation of the prime factors of k with multiplicity is congruent mod k to the reverse of k.

Terms for which the common value of A103168(k) and A340592(k) is prime include 14, 50, 194, 1100, and 116416.

LINKS

Robert Israel, Table of n, a(n) for n = 1..2200

EXAMPLE

a(7) = 14 is a term because A103168(14) = 41 mod 14 = 13 and A340592(14) = 27 mod 14 = 13.

MAPLE

revdigs:= proc(n) local L, i;

L:= convert(n, base, 10);

add(L[-i]*10^(i-1), i=1..nops(L))

end proc:

f:= proc(n) local L, p, i, r;

L:= sort(map(t -> t[1]$t[2], ifactors(n)[2]));

r:= L[1];

for i from 2 to nops(L) do r:= r*10^(1+max(0, ilog10(L[i])))+L[i] od;

end proc:

f(1):= 1:

select(n -> (f(n) - revdigs(n)) mod n = 0, [$1..20000]);

PROG

(Python)

from sympy import factorint

def A103168(n):

return int(str(n)[::-1])%n

def A340592(n):

if n == 1: return 0

return int("".join(str(f) for f in factorint(n, multiple=True)))%n

def ok(n):

return A103168(n) == A340592(n)

print([k for k in range(1, 20000) if ok(k)]) # Michael S. Branicky, Jan 18 2022

CROSSREFS

Includes A002385. Cf. A004086, A037276, A103168, A340592.

Sequence in context: A262371 A359683 A184642 * A094252 A209038 A182803

Adjacent sequences: A350833 A350834 A350835 * A350837 A350838 A350839

KEYWORD

nonn,base

AUTHOR

J. M. Bergot and Robert Israel, Jan 17 2022

STATUS

approved